(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Two identical charges q are placed on the x axis, one at the origin and the other at x = 5 cm. A third charge -q is placed on the x axis so the potential energy of the three-charge system is the same as the potential energy at infinite separation. Its x coordinate is: (x=13)

2. Relevant equations

I know the correct answer to this one because I'm looking over a marked up test in preparation for the final.

I've been using the equations for the electric potential energy of a system of point charges:

[tex]U=W=k\frac{q_{1}q_{2}}{r}[/tex]

3. The attempt at a solution

...and expanding that to the work of the entire system:

[tex]W=0=W_{12}+W_{23}+W_{13}[/tex]

so,

[tex]W=0=k\frac{q_{1}q_{2}}{5}+k\frac{q_{2}q_{3}}{d}+k\frac{q_{1}q_{3}}{5+d}[/tex]

Since [tex]q_{3}[/tex] is negative, simplify:

[tex]W=0=k\frac{q^{2}}{5}-k\frac{q^{2}}{d}-k\frac{q^{2}}{5+d}[/tex]

I might be missing something simple in algebra, but I can't figure out how to simplify this down enough to solve for [tex]d[/tex].

Any ideas? Am I even on the right track here?

Thanks!

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# Homework Help: Potential Energy of a system of Point Charges

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